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Beliebt Rechnen >

integral from 0 to ln(2) of sqrt(e^x-1)

Lösung

\int_{0}^{l n (2)} e^{x} - 1 d x

Lösung

2 (- \frac{π}{4} + 1)

+1

Dezimale

0.42920 \dots

Schritte zur Lösung

\int_{0}^{l n (2)} e^{x} - 1 d x

Wende U-Substitution an

= \int_{1}^{2} \frac{u - 1}{u} d u

Wende U-Substitution an

= \int_{0}^{1} \frac{2 v ^{2}}{v ^{2} + 1} d v

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{1} \frac{v ^{2}}{v ^{2} + 1} d v

\frac{v ^{2}}{v ^{2} + 1} = - \frac{1}{v ^{2} + 1} + 1

= 2 \cdot \int_{0}^{1} - \frac{1}{v ^{2} + 1} + 1 d v

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (- \int_{0}^{1} \frac{1}{v ^{2} + 1} d v + \int_{0}^{1} 1 d v)

\int_{0}^{1} \frac{1}{v ^{2} + 1} d v = \frac{π}{4}

\int_{0}^{1} 1 d v = 1

= 2 (- \frac{π}{4} + 1)

Graph

Beliebte Beispiele

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d er i v a t i v e y = (6 x + 5)^{2}

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\frac{\partial}{\partial x} (\frac{x}{( x ^{2} + y ^{2} + z ^{2} )})

y^{''}-xy^'+y=0

y^{^{''}} - x y^{^{'}} + y = 0

integral of (x^{1/3})

\int (x^{\frac{1}{3}}) d x

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d er i v a t i v e f (x) = x (x + 3)^{3}